Question

Once Kate's kite reaches a height of 60 ft (above her hands), it rises no higher but drifts due east in a wind blowing 4 ft divided by s. How fast is the string running through Kate's hands at the moment that she has released 106 ft of string?

Answer 1

Answer: The string is running through Kate's hand at 13.19 ft/ sec.

Step-by-step explanation:

Since we know that

$z^2=x^2+y^2\\\\x=\sqrt{z^2-y^2}$

y = 60 feet

dx = 4 ft/sec

z=106 feet

we need to find the value of dz.

$d(z^2=x^2+y^2)\\\\2z.dz=2x.dx\\\\dz=\dfrac{x.dx}{z}\\\\dz=\dfrac{\sqrt{z^2-y^2}.dx}{z}\\\\dz=\dfrac{\sqrt{106^2-60^2}.4}{106}\\\\dz=\dfrac{349.53\times 4}{106}\\\\dz=13.19$

Hence, the string is running through Kate's hand at 13.19 ft/ sec.